A water taxi travels around an island in a path that can be modeled by the equation y =0.5(x - 16). A water skier is skiing along a path that begins at the point
(6,6) and ends at the point (8. - 4).
a. Write a system of equations to model the problem.
b. Is it possible that the water skier could collide with the taxi? Explain

Answers

Answer 1

I realize that the equation is different, but do it in the same way, it'll help! It is given that the water​ taxi's path can be modeled by the equation y =0.5(x - 14)^2. ​Therefore, this is one of the equations in this system. Find a linear equation that will model the path of the water​ skier, which begins at the point (6,6) and ends at the point (8,-4). The slope is (-5). Use the slope and one point on the line to find the​ y-intercept of the line.  The​ y-intercept of the line that passes through the points (6,6) and (8,-4) is (0,36). Thus, the equation is y=-5x+36. Now, to determine if it is possible for the water skier to collide with the​ taxi, we have to determine if there is a solution to the system of equations. To determine if there is a solution to the system of​ equations, solve the system using substitution.​ First, write the equation that models the water​ taxi's path in standard form. y=0.5(x - 14)^2-->0.5x^2-14x+98. Use substitution. Substitute for  y in the equation and then solve for  x. As the expression on the left side of the equation cannot easily be​ factored, use the Quadratic Formula to solve for x. Do x=-b(plusorminus)sqrrtb^2-4ac/2a. Identify a, b, and c. a=0.5, b=-9, and c=62. Substitute into the Quadratic Formula. If there is a negative number under the radical, there are NO solutions. Thus, the path of the water skier will never cross the path of the taxi.

In conclusion: It is not possible that the water skier could collide with the taxi as the two paths never cross.


Related Questions

Please help me 32 points
Problem
Choose the inequality that represents the following graph.

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Answer:

im pretty sure its d

Step-by-step explanation:

pretty sure it’s d; i think

Please help me I can’t seem to figure this out


7.01 x 0.356

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Answer:

2.49556

Step-by-step explanation:

Answer:

2.49556

Step-by-step explanation:

0.356

× 7.01

---------

2.49556

Which of the following is not one of the five elements of hip-hop culture?

A. DJ-ing
B. Disco dancing <<
C. Graffiti art
D. MC-ing

answer : B

I hope this helped !

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It’s b I hope I helped u with this I took the quiz

Which of the following is true about similar figures?

All similar figures are congruent.


If two figures are not similar, they can still be congruent.


All congruent figures are similar.


If two figures are not congruent, they can't be similar.

Answers

Answer:

All congruent figures are similar

Step-by-step explanation:

Congruent means "same" in mathematics and you have evidence to prove it. You can look at two puppies with the exact same fur color and be like "yeah they're the same". If they are the same size and shape they're congruent. This is why the AAA postulate can't work because triangles can have the same angles yet be different sizes. If figures are not congruent, they can't be similar and figures that aren't similar can't be congruent either.

All similar figures are congruent is true about similar figures

What is congruency?

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

In mathematics, congruent means identical, and you can cite examples to support your claim.

just by looking at them. They are congruent if their dimensions match. Triangles can have the same angles but differ in size, which makes the AAA postulate invalid.

If two figures are not similar, they cannot be congruent, therefore similarly unrelated figures cannot be congruent.

learn more about congruency here :

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(3x + 3x²) + (2x² + 2x)?​

Answers

Answer:

=5x2+5x

Step-by-step explanation:

Let's simplify step-by-step.

3x+3x2+2x2+2x

Use the distributive property to remove the parentheses. -5(-6y - 3w + 2)

Answers

Answer:

−5(−6y−3w+2)

=(−5)(−6y+−3w+2)

=(−5)(−6y)+(−5)(−3w)+(−5)(2)

=30y+15w−10

=15w+30y−10

The distance between two towns is 75 km. The distance between the two towns on a map is 1.5 cm. What is the scale on the map?

Scale = 1cm :
km

Answers

Answer:

50

..................

Step-by-step explanation:

1.5cm => 75km

1cm => 75km * (1/1.5) = 50km

Hence the scale of the map is 1cm : 50km.

The product of t and 6 is greater than 12

Answers

Answer:

A possible answer for t could be 3

Step-by-step explanation:

I honestly don't know if this is right, but yeah here ya go!

All values of t which are greater than 2 , are the solutions of given inequality.

Inequality :

It is given that,

The product of t and 6 is greater than 12.

So that, inequality is,

                    [tex]6*t > 12[/tex]

Divide both side by 6.

                 [tex]6*t > 12\\\\t > \frac{12}{6} \\\\t > 2[/tex]

Therefore, all values of t which are greater than 2 , are the solutions of given inequality.

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If bc+ad=b solve for a

Answers

Answer:

a = (b - bc)/d

Answer:

ad=b-bc

a=b-bc/d or  a=b-bc

                        --------

                            d

*everything is divided by d on the other side...so b-bc is all divided by d

Carl earns $75 washing 5 dogs. At this rate, how much does Carl earn washing 4 dogs?​

Answers

$60 to wash four dogs

Answer:

$60

Step-by-step explanation:

75÷5=15, meaning he earns $15 per dog so if we do 15×4 we end up with 60 dollars

Help me with this answer I know there is no solution I just wanna know why

Answers

Answer:

The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. ... This is because there is truly no solution—there are no values for x that will make the equation true

Answer:

No solution

Step-by-step explanation:

The solution x = 0 means that the value 0. “No solution” means that there is no values

George earns commission as a percentage of his tuxedo sales. On Tuesday, he sold $750 worth of tuxedos and earned $60
commission. What is George's commission rate?

Answers

Answer:

8%

Step-by-step explanation:

1% of 750 is 7.50

So 60 divided by 7.5 is 8

Becca’s dog walking business started with 1 dog. She walks 2 additional dogs each month.
The graph represents the problem. How many dogs does she walk in the third month?

Answers

Answer:

7 is the correct answer

2 each month + 1 that she started of with = 7 I hope this helped.

2y+ 3 = 15
I have to solve for y but it is complicated

Answers

Answer:

y=6

Step-by-step explanation:

2y = 15 - 3

2y = 12

y = 6

I hope this helps

2y+3=15
2y+3-3=15-3
y=6

Natalia bought 888 glitter wands for \$50$50dollar sign, 50.
Determine whether or not each wand purchase below has the same price per wand as glitter wands.

Has the same price per wand as glitter wands
Does not have same price per wand as glitter wands
444 sparkle wands for \$20$20dollar sign, 20
666 fairy wands for \$37.50$37.50dollar sign, 37, point, 50
101010 glow wands for \$65$65dollar sign, 65

Answers

9514 1404 393

Answer:

  6 for $37.50 has the same price

Step-by-step explanation:

The price per wand is found by dividing the price by the number of wands.

  8 for $50   ⇒   $50/8 = $6.25 per wand

__

  4 for $20   ⇒   $20/4 = $5.00 per wand   not the same

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  10 for $65   ⇒   $65/10 = $6.50 per wand   not the same

What is the volume of the rectangular pyramid

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Answer:

Image result for What is the volume of the rectangular pyramid

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Finding the Volume of a Rectangular Pyramid

Your overall formula for finding the volume of these multi-faceted shapes is V = (l x w x h) / 3. Basically, your first step is finding the area of the base by multiplying length by width. Once you determine the area of the base, multiply that by the height.

Answer:

Finding the Volume of a Rectangular Pyramid

Your overall formula for finding the volume of these multi-faceted shapes is V = (l x w x h) / 3. Basically, your first step is finding the area of the base by multiplying length by width. Once you determine the area of the base, multiply that by the height.

Step-by-step explanation:

question 15: Given l∥m, find the value of x.

Answers

Answer:

x=8

Step-by-step explanation:

the addition of all the angles must equal 360(the 4 angles on the intersection) degrees

125+125=250

360-250=110

110/2=55

7*8-1=55

Which of the following coordinates is located in Quadrant IV

Answers

Answer:

Is there a picture?

Step-by-step explanation:

Answer: where is the picture

Step-by-step explanation:

but the 4th Quadrant is all the way to the right bottom

Ben has been driving nonstop along a highway for 5 hours: The minimum speed permitted on the highway is 45 kph and the maximum speed permitted is 70 kph.Solve for the range of the distances d that Ben could trave legally traveled. Give your answer as an inequality.

Answers

Answer:

[tex]225\leq d \leq 350[/tex]

Step-by-step explanation:

5 * 45 = 225

5 * 70 = 350

Help with these questions I´ll CASHAPP YOU 55$$

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Answer:

umm ok srry this is confusing

Step-by-step explanation:

Help with these questions I´ll CASHAPP YOU 55$$ can anybody help plz plz?????

I need help with this question! Will mark brainliest :)

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Answer:

hiii

your answer is option d

HOPE IT HELPS YOU OUT PLEASE MARK IT AS BRAINLIEST AND FOLLOW ME PROMISE YOU TO FOLLOW BACK ON BRAINLY.IN

answer: y= 20x+30

Step-by-step explanation:

it says they charge 20$ per hour and x is the amount of hours.

30$ is charged as the registration fee at the beginning only.

Sophia saves $30 every month to her savings account. She withdrew $120 one time to go Christmas shopping. She now has $330 in her account. How many months has she been saving money?

Answers

Answer:

15 months

Step-by-step explanation:

330+120=450, and 450 divided by 30 equals 15. Therefore, Sophia has saved $30 to her savings account every month for 15 months.

Give an example of a rational number that is NOT a whole number.

Answers

Answer:

−3, 8, 32, 7, -5

Step-by-step explanation:

Mario’s pizzeria makes an average of 23 pizzas per hour during this week. What is the probability that Mario will make 21 pizzas during an hour this week?

0.079
0.076
0.0000000027
0.073

Answers

0.076? I think so and I’m very sorry if I’m wrong

Six calculators cost 180 determine the cost per calculator

Answers

Each calculator would cost 30 dollars (sorry if this isn't what you mean)

A statistics teacher announces to the class at the beginning of the semester that there is a 40% chance that a randomly chosen student will finish the semester with an A in the class and there is a 60% that a randomly chosen student will get an A on a test during the semester. Is the probability that a randomly chosen student receives an A in the class and an A on a test during the semester equal to 0.24? Yes, because the chance of getting an A on a test and getting an A in the class are mutually exclusive. Yes, because the chance of getting an A on a test and getting an A in the class are mutually exclusive. No, because the chance of getting an A on a test and getting an A in the class are not independent. No, because the chance of getting an A on a test and getting an A in the class are not independent. Yes, because the chance of getting an A on a test and getting an A in the class are independent. Yes, because the chance of getting an A on a test and getting an A in the class are independent. No, because the chance of getting an A on a test and getting an A in the class are not mutually exclusive.

Answers

Answer:

c. No, because the chance of getting an A on a test and getting an A in the class are not independent.

Step-by-step explanation:

brainly?


Solve the system of inequalities graphically. Which point is in the solution?
y2x-4
y S-2x - 8

Answers

Answer:

(d). ( - 4, 0 )  

Step-by-step explanation:

(a). ( 5 , - 2 ) --- Coordinates do not satisfy both inequality.

(b). ( - 2 , - 8 ) --- Coordinates satisfy y ≤ - 2x - 8, but do not satisfy y ≥ x - 4 .

(c). ( 0 , 0 ) --- Coordinates satisfy y ≥ x - 4, but do not satisfy y ≤ - 2x - 8 .

(d). ( - 4, 0 ) --- The solution of the task.

A plumber charges a one-time fee of $75 plus a fixed hourly rate, h, in dollars. The plumber works at a customer's house for 2 hours and charges a total of $205.



What is the fixed hourly rate, in dollars, that the plumber charges?

Answers

Answer:

$65

Step-by-step explanation:

$205 - $75 = $130

$130 / 2 hours = $65

The hourly rate, in dollars, is $65 per hour.

56 gallons to 77 gallons​

Answers

Answer: it would be +21 gallons

Step-by-step explanation:you have to add 21 gallons to get 77 gallons

The Awnser is +21gallons

please answer i will give you brainiest!!!!!!!!!!!!!!!!!!

Answers

Answer:

I'm pretty sure it's A because its showing that the line starts from 1 and goes up if that makes sense.

Answer:

B

Step-by-step explanation:

x < 1 means that x is lesser than 1. A shows x is more than 1 so it is wrong. C shows x is more than -1 which is not entirely true since x could be more than -1, but not less than 1. However, the line in C stretches all the way to 8 which is more than 1 so it is wrong.  D shows that x is lesser than -1, but x could have been 0 or -1, so it is not true either.

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